teaching, math, teaching math

The Social Construction of Mathematics

To illustrate an early lesson in white racial framing, imagine that a white mother and her child are in the grocery store. The child sees a black man and shouts out, “Mommy, that man’s skin is black!” Several people, including the black man, turn to look. How do you imagine the mother would respond? Most people would immediately put their finger to their mouth and say, “Shush!” When white people are asked what the mother might be feeling, most agree that she is likely to feel anxiety, tension, and embarrassment. Indeed, many of us have had similar experiences wherein the message was clear: we should not talk openly about race.

-Robin DiAngelo in “White Fragility” p. 37

“Race is just a social construction,” is a common refrain in some circles. But what does that actually mean?

Robin DiAngelo’s example in White Fragility illustrates one of the many ways that race is socially constructed. In her anecdote, a child learns that race is not to be talked about in public. The child might also learn that being black is something negative or to be embarrassed of — the mother acts the same as she might if the child pointed out someone was overweight or disfigured, rather than particularly good-looking or well-dressed. Lessons about race become part of the fabric of society because of these everyday interactions. Our language, choices, and responses shape our perspectives and the perspectives of those around us.

The phrase, “Well, race is just a social construction,” is interesting in its use of the passive voice. Race is socially constructed, but who constructed it? Well, all of us, every day. And if it has been made, it can be remade. Mathematics is the same, as are race, gender, and more in the context of the mathematics classroom. Mathematics is what it is because of people, and as Rochelle Gutierrez says, mathematics needs people as much as people need mathematics. The learning of mathematics has changed dramatically over time, more than most realize. It will continue to change. What are some questions one might ask to reconstruct mathematics in a way that better humanizes and values all students?

We spend countless hours worrying about kids understanding fractions — to this day, I am still completely flummoxed by that — and close to no time folding in math history. Somehow ensuring kids can add fractions with denominators nobody cares about is more important than humanizing math education with the hundreds of artists — spanning every culture/civilization on the planet — that have contributed to its creation?

Both Thales, the legendary founder of Greek mathematics, and Pythagoras, one of the earliest and greatest Greek mathematicians, were reported to have travelled widely in Egypt and Babylonia and learnt much of their mathematics from these areas. Some sources even credit Pythagoras with having travelled as far as India in search of knowledge, which may explain some of the close parallels between Indian and Pythagorean philosophy and geometry.

And for a lot of students it feels like “just pretend.” Just pretend this is real world. Even though students might feel like “this doesn’t look like anything that’s in my real world.” And that’s where we get that question. “When are we ever gonna use this?” Now the question of “When are we ever gonna use this?” has already been asked by that person, many times. In their head, they’ve said, “When am I gonna use this?” “When are we gonna use this?” comes up when they’re basically asking everyone else in the room to recognize and to comment on the fact that the emperor isn’t wearing any clothes.

These are only a few of the questions one might ask. What am I missing?

Some Things I Believe To Be True

Acting and not acting are both actions; nothing is neutral.

-Imani Goffney

Most humans dislike mathematics — and not only dislike mathematics, but believe that they are intrinsically unable to learn or practice mathematics — but I think we can do better.

A narrow subset of mathematics as it is taught in schools is not the only cause, but it may be one.

Humans could have constructed a largely different mathematics; the mathematics we have is in many ways an accident of history.

Speaking as a high school teacher, much of what we teach is not essential for students to learn. While I believe that what I teach helps students learn to think mathematically, it is not the only means to that end.

Asking hard questions about the nature of mathematics is a worthwhile exercise.

I’m not advocating for a new mathematics tomorrow. Instead, I want to push myself to find the small moments — small moments that, when added together, send important messages — to make small changes. Stopping to talk about a mathematician who doesn’t look like what a student might expect a mathematician to look like. Pausing to acknowledge the rich intellectual history of a topic. Unpacking the ways race and gender play out in math classrooms, and interrogating why things are the way they are. Searching out ambiguity and inconsistency to validate students’ experiences that mathematics is not, to them, the system of pure logic it has been made out to be. Seizing on moments of authentic discovery, and helping students to feel what it might be like to practice mathematics. Questioning why we learn what we learn, opening avenues for dissent, and helping students imagine what else mathematics might be in the future.

Whether I realize it or not, everything I do influences student beliefs about mathematics. I can choose to ignore these questions and entrench the status quo, or start to find ways to communicate new values and new perspectives.

Coda: On Competence

In discussing on Twitter some of the ideas that came together as this blog post, I was accused of being a bad teacher because asking questions like these would just confuse students and leave them feeling even more helpless in math class than they did before. I think it’s worth asking hard questions, but what are the trade-offs of complicating a subject so many students already dislike?

Mathematics is made by people. Who will take the opportunity to remake it? I want students to see the richness that mathematics is, and that it might be. But I also have a responsibility to help students be successful within the parameters of the system we have. I think that the most powerful thing I can do for a young person is to help them develop a sense of mathematical competence: to recognize the ways that they are mathematically smart, and to create space for those smartnesses to flourish in my classroom. And, inevitably, most of those smartnesses will reflect mathematics as it is, not mathematics as it might be. I’m not advocating for radical change. Instead, I’m advocating for great everyday teaching that helps students gain the skills they need and recognize the incredible talents they have. At the same time, there are innumerable opportunities to ask hard questions and engage students with the tensions inherent in mathematics education. Those opportunities, taken judiciously and purposefully, can only expand the pool of students who see themselves as potential mathematicians, and expand the discipline that students are learning.

3 thoughts on “The Social Construction of Mathematics”

“…much of what we teach is not essential for students to learn. While I believe that what I teach helps students learn to think mathematically, it is not the only means to that end.” Whooo boy.

There’s such a tension here among our purposes. (a) Prepare learners for careers that require calculus, (b) share mathematics as a human endeavor, and (c) use mathematics as a context for reasoning and problem solving. So much of what we require is because of (a). So much of what we do is because that is not relevant to all learners, and might not even look relevant to the audience of future engineers and scientists. I think we find that (b) helps make (a) more palatable, and has a lot of connections to (c).

Involving the learner in the construction of mathematics really motivates (c), which I think would serve purposes (b) and even (a) better.

Thanks, John! They’re fun questions to think about. I love the idea of articulating the different, at times conflicting purposes of mathematics education and teasing out how to align them in support of each other as much as possible.